Electing an Approximate Center in a Huge Modular Robot with the k-BFS SumSweep Algorithm

Among the diversity of the existing modular robotic systems, we consider in this paper the subset of distributed modular robotic ensembles composed of resource-constrained identical modules that are organized in a lattice structure and which can only communicate with neighboring modules. These modular robotic ensembles form asynchronous distributed embedded systems. In many algorithms dedicated to distributed system coordination, a specific role has to be played by a leader, i.e., a single node in the system. This leader can be elected using various criteria. A possible strategy is to elect a center node, i.e., a node that has the minimum distance to all the other nodes. Indeed, this node is ideally located to communicate with all the others and this leads to better performance in many algorithms. The contribution of this paper is to propose the $k$-BFS SumSweep algorithm designed to elect an approximate-center node. We evaluated our algorithm both on hardware modular robots and in a simulator for large ensembles of robots. Experimental results show that k-BFS SumSweep is often the most accurate approximation algorithm (with an average relative accuracy between 90% to 100%) while using the fewest messages in large-scale systems, requiring only a modest amount of memory per node, and converging in a reasonable length of time.